The invention relates to companding, i.e., the compression and expansion of the dynamic range of electrical signals.
In companding, an input signal is compressed so that the dynamic range of the compressed signal is reduced as compared with that of the input signal. After desired transmission or processing, the dynamic range of the signal is expanded. Noise picked up in transmission or processing then has reduced amplitude.
Companding may be considered as originating in the field of telephone signal transmission. It is also used in acoustical recording and playback, where so-called Dolby systems and the like have found widespread use in high-fidelity reproduction. Such systems can reproduce sound with reduced noise.
Companding is being used in other devices, such as hearing aids, for example, where power consumption must be minimized. Low-power devices are particularly susceptible to noise.
Such concerns also apply generally to today""s integrated circuits, which usually must operate with small voltage swings and thus are vulnerable to noise. This is true especially of high-Q filters, in which large internal gains can amplify noise and interference.
The following published items are representative of the state of the art:
1. Y. P. Tsividis et al., xe2x80x9cCompanding in Signal Processingxe2x80x9d, Electronics Letters, Vol. 26 (1990), pp. 1331-1332;
2. F. Callias et al., xe2x80x9cA Set of Four IC""s in CMOS Technology for a Programmable Hearing Aidxe2x80x9d, IEEE Journal of Solid-State Circuits, Vol. 24 (1989), pp. 301-312;
3. E. Seevinck, xe2x80x9cCompanding Current-mode Integrator: a New Circuit Principle for Continuous-time Monolithic Filtersxe2x80x9d, Electronics Letters, Vol. 26 (1990), pp. 2046-2047;
4. D. R. Frey, xe2x80x9cLog-domain Filtering: an Approach to Current-mode Filteringxe2x80x9d, IEEE Proceedings-G, Vol. 140 (1993), pp. 406-416;
5. E. Dijkstra et al., xe2x80x9cLow-Power Oversampled A/D Convertersxe2x80x9d, in Van de Plassche et al. (eds.), Analog Circuit Design: Low-power Low-voltage, Integrated Filters, and Smart Power, Kluwer, Boston, 1995.
Among these items, 3., 4. and 5. are concerned with xe2x80x9cinstantaneous compandingxe2x80x9d, in which companding is effected based on a signal""s instantaneous value. By distinction, items 1. and 2. are concerned with xe2x80x9csyllabic compandingxe2x80x9d, depending on some measure of a signal""s average strength in a suitably chosen time interval.
Of particular present interest in electrical signal processing are filter circuits with companding, and with linear input-output response. Among the above-referenced items, 3. and 4. disclose special cases of such circuits.
Quite generally, for a continuous-time linear, time-invariant filter or signal-processor circuit as described by state equations in the standard form
{dot over (x)}=Ax+Bu
and
y=Cx+Du
where u(t) is the input vector, y(t) the output vector, x(t) the state vector, and A, B, C and D are matrices of appropriate dimensions, it would be desirable to have a technique for producing a circuit with internal companding and with the same input-output response as the specified circuit.
In the case of a continuous-time filter or signal processor, such a companding circuit can be realized by implementing, instead of the specified circuit, a circuit described by state equations
{dot over (w)}=Âw+{circumflex over (B)}u
and
y=Ĉw+Du
for a derived state vector w(t)=G(t)x(t) of derived state variables, and for matrices
Â={dot over (G)}Gxe2x88x921+GAGxe2x88x921, {circumflex over (B)}=GB
and
Ĉ=CGxe2x88x921
wherein the nonsingular, differentiable matrix G(t) has been determined such that the derived state vector w(t) is companded for reduced noise as compared with the state vector x(t). It can be verified by substitution that the derived new circuit is input-output equivalent to the originally specified, internally linear circuit.
In this description, t denotes time, and a xe2x80x9cdotxe2x80x9d superposed on a symbol designates taking the derivative with respect to time of the entity denoted by the symbol under the dot. When applied to a vector or a matrix, the derivative is understood component- or element-wise.
In the case of a discrete-time filter or signal processor, described by state equations
x(n+1)=Ax(n)+Bu(n)
and
y(n)=Cx(n)+Du(n)
where integers n and n+1 refer to consecutive instants of discrete time, new circuit matrices are determined by
Â=G(n+1)AGxe2x88x921(n), {circumflex over (B)}=G(n+1)B
and
Ĉ=CGxe2x88x921(n).
It can be verified by substitution that the derived new circuit is input-output equivalent to the originally specified, internally linear circuit.